Lévy processes and stochastic calculus
By: David Applebaum.
Edition: 2nd ed.
Series: Cambridge studies in advanced mathematics -- 116
Publisher: Cambridge University Press
Published: 2009
Place of publication: Cambridge; New York
Language: eng
Number of pages: 460
ISBN-13: 9780521738651
Subjects: Lévy processes; Stochastic analysis
Description: Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.
Notes: Includes bibliographical references (p. 431-448) and indexes.